The book presents a thorough treatment of the central ideas and their applications of Kolmogorov complexity with a wide range of illustrative applications, and will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics.Expand

A new theory of similarity between words and phrases based on information distance and Kolmogorov complexity is presented, which is applied to construct a method to automatically extract similarity, the Google similarity distance, of Words and phrases from the WWW using Google page counts.Expand

A new "normalized information distance" is proposed, based on the noncomputable notion of Kolmogorov complexity, and it is demonstrated that it is a metric and called the similarity metric.Expand

How do we measure similarity-for example to determine an evolutionary distance or to detect clusters-in data of arbitrary type? We develop a general mathematical theory of universal similarity. We… Expand

Evidence of successful application in areas as diverse as genomics, virology, languages, literature, music, handwritten digits, astronomy, and combinations of objects from completely different domains, using statistical, dictionary, and block sorting compressors is reported.Expand

This work shows that the information distance is a universal cognitive similarity distance, and investigates the maximal correlation of the shortest programs involved, the maximal uncorrelation of programs, and the density properties of the discrete metric spaces induced by the information distances.Expand

The goodness-of-fit of an individual model with respect to individual data is precisely quantify and it is shown that-within the obvious constraints-every graph is realized by the structure function of some data.Expand

Here we present in a single essay a combination and completion of the several aspects of the problem of randomness of individual objects which of necessity occur scattered in our texbook"An… Expand